XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-94-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 21 12.46 12.00 112,102 MAX VALUE 22,508.10 2.49 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 354.00 0.00 -1,054.11 0.06 0.17 1.82

Tightness 0.44 0.56 0.50 0.50 90.32 0.00 -124.27 0.02 0.04 3.65

Tuples 278 353 311.39 312.00 56,051 MAX VALUE 1,033.25 12.19 0.04 3.65

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 14 9.00 9.00 360 3.55e+37 86.46 2.30 0.26 1.97

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	21	12.46	12.00	112,102	MAX VALUE	22,508.10	2.49	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	354.00	0.00	-1,054.11	0.06	0.17	1.82
Tightness	0.44	0.56	0.50	0.50	90.32	0.00	-124.27	0.02	0.04	3.65
Tuples	278	353	311.39	312.00	56,051	MAX VALUE	1,033.25	12.19	0.04	3.65
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	9.00	360	3.55e+37	86.46	2.30	0.26	1.97
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 9
Tree depth: 4
CIR: 0.10
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 6 55 22.40 18.50 448 1.52e+25 57.99 14.58 0.65 2.65

Variables per cluster 5 21 11.50 10.50 230 2.75e+20 47.06 4.92 0.43 2.25

Separator constraints 0 41 13.40 10.00 268 0 None 12.59 0.94 2.55

Separator variables 0 19 9.50 8.50 190 0 None 4.92 0.52 2.25

Clusters per var 1 11 5.75 6.50 230 3.25e+24 56.44 3.76 0.65 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	55	22.40	18.50	448	1.52e+25	57.99	14.58	0.65	2.65
Variables per cluster	5	21	11.50	10.50	230	2.75e+20	47.06	4.92	0.43	2.25
Separator constraints	0	41	13.40	10.00	268	0	None	12.59	0.94	2.55
Separator variables	0	19	9.50	8.50	190	0	None	4.92	0.52	2.25
Clusters per var	1	11	5.75	6.50	230	3.25e+24	56.44	3.76	0.65	2.16

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 135
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 32 348 122.76 93.00 4,665 MAX VALUE 175.25 81.06 0.66 3.56

Variables per cluster 11 84 29.00 21.50 1,102 MAX VALUE 121.70 18.62 0.64 3.12

Separator constraints 0 187 82.08 70.00 3,119 0 None 48.91 0.60 3.28

Separator variables 0 64 24.26 19.50 922 0 None 14.15 0.58 3.01

Clusters per variable 1 11 6.12 7.00 1,102 MAX VALUE 295.97 2.73 0.45 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	32	348	122.76	93.00	4,665	MAX VALUE	175.25	81.06	0.66	3.56
Variables per cluster	11	84	29.00	21.50	1,102	MAX VALUE	121.70	18.62	0.64	3.12
Separator constraints	0	187	82.08	70.00	3,119	0	None	48.91	0.60	3.28
Separator variables	0	64	24.26	19.50	922	0	None	14.15	0.58	3.01
Clusters per variable	1	11	6.12	7.00	1,102	MAX VALUE	295.97	2.73	0.45	2.19

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 150
Triangles: 119
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.13 0.47 0.23 0.22 9.31 0.00 -60.06 0.07 0.30 2.93

Degree 4 14 9.00 9.00 360 3.55e+37 86.46 2.30 0.26 1.97

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.29 3.00 493 MAX VALUE 177.16 0.45 0.14 0.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.13	0.47	0.23	0.22	9.31	0.00	-60.06	0.07	0.30	2.93
Degree	4	14	9.00	9.00	360	3.55e+37	86.46	2.30	0.26	1.97
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.29	3.00	493	MAX VALUE	177.16	0.45	0.14	0.60

Triangulated primal graph

Density: 51.28%
MCB compute time (ms): 11
MCB cycles: 373
Triangles: 2,380

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.68 1.00 0.83 0.81 33.40 0.00 -7.55 0.11 0.13 3.13

Degree 4 30 20.00 24.50 800 MAX VALUE 113.20 9.43 0.47 2.56

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,119 MAX VALUE 409.78 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.68	1.00	0.83	0.81	33.40	0.00	-7.55	0.11	0.13	3.13
Degree	4	30	20.00	24.50	800	MAX VALUE	113.20	9.43	0.47	2.56
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,119	MAX VALUE	409.78	0.00	0.00	0.00

Dual graph

Density: 9.60%
MCB compute time (ms): 435
MCB cycles: 1,695
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.45 0.64 0.50 0.50 90.26 0.00 -124.47 0.03 0.05 3.95

Degree 10 25 17.18 17.00 3,092 MAX VALUE 508.53 3.21 0.19 2.53

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.23 3.00 5,474 MAX VALUE 1,972.18 0.46 0.14 0.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.64	0.50	0.50	90.26	0.00	-124.47	0.03	0.05	3.95
Degree	10	25	17.18	17.00	3,092	MAX VALUE	508.53	3.21	0.19	2.53
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.23	3.00	5,474	MAX VALUE	1,972.18	0.46	0.14	0.58

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 75
MCB cycles: 141

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 5 3.56 3.00 640 MAX VALUE 224.53 0.72 0.20 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.87 7.00 969 MAX VALUE 269.65 1.12 0.16 1.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.00	0.00	0.00	0.00	0.00	None	0.00	None	0.00
Degree	2	5	3.56	3.00	640	MAX VALUE	224.53	0.72	0.20	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.87	7.00	969	MAX VALUE	269.65	1.12	0.16	1.47

Triangulated dual graph

Density: 46.49%
Triangles: 198,398

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.70 1.00 0.84 0.81 150.42 0.00 -33.29 0.09 0.11 4.47

Degree 10 130 83.22 101.50 14,980 MAX VALUE 759.48 40.99 0.49 3.94

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.70	1.00	0.84	0.81	150.42	0.00	-33.29	0.09	0.11	4.47
Degree	10	130	83.22	101.50	14,980	MAX VALUE	759.48	40.99	0.49	3.94
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.68%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.45 1.00 0.79 0.74 142.89 0.00 -45.07 0.16 0.20 3.37

Degree 2 64 20.90 7.00 3,762 MAX VALUE 423.18 22.79 1.09 3.04

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.79	0.74	142.89	0.00	-45.07	0.16	0.20	3.37
Degree	2	64	20.90	7.00	3,762	MAX VALUE	423.18	22.79	1.09	3.04
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 44
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-94-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 14 3.27 2.00 720 MAX VALUE 211.23 2.87 0.88 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.48 6.00 914 MAX VALUE 262.42 0.86 0.13 0.55

XCSP 2.1 Benchmarks